ABSTRACT: We will consider the approximation by a spectral method of the
solution of the Cauchy problem for a scalar strictly nonlinear hyperbolic
equation in one dimension posed in the whole real line. We will analyze a
spectral viscosity method in which the orthogonal basis considered is the
one of Hermite functions. We will show results of convergence of the
approximate solution to the unique entropy solution of the problem which are
obtained by using compensated compactness arguments. Some numerical examples
will also be presented.